6.05B: Enzyme Reaction Mechanisms - Quantiative Analyses of Serine Protease Catalysis

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Learning Goals (ChatGPT o1, 1/30/25)

Mechanistic and Structural Insights

• Integrate Multiple Data Types:
  • Explain how structural (PDB data), kinetic, and thermodynamic data combine to elucidate enzyme reaction mechanisms.
• Identify Key Catalytic Residues:
  • Describe the roles of Ser 195, His 57 (or His 95 in some texts), and Asp 102 in the catalytic triad of serine proteases.
• Interpret Enzyme–Substrate Interactions:
  • Analyze how changes in the substrate (e.g., leaving group modifications) provide evidence for the formation of a covalent acyl-enzyme intermediate.

Kinetic Analysis and Reaction Mechanisms

• Understand Kinetic Parameters:
  • Interpret kinetic constants (kcat, Km, and kcat/Km) and relate them to specific steps in the enzyme mechanism (acylation vs. deacylation).
• Distinguish Reaction Mechanisms:
  • Explain the concept of a BiBi Ping Pong reaction and how kinetic bursts (rapid formation of an intermediate followed by a slower reaction phase) support this mechanism.
• Apply Mathematical Models:
  • Simplify complex kinetic equations (e.g., under the rapid equilibrium assumption) to describe enzyme kinetics for ester versus amide hydrolysis.

Effects of Experimental Variables

• Impact of pH and Ionic Strength:
  • Use pH-dependent kinetic data to identify the roles of ionizable groups (e.g., histidine as a general base) in enzyme activity.
• Enzyme Modification Strategies:
  • Evaluate how site-specific mutagenesis and chemical modification (e.g., using DIPF or chloromethyl ketones) confirm the roles of individual amino acids in catalysis.
• Solvent Effects on Enzyme Activity:
  • Compare enzyme function in aqueous versus nonaqueous (organic) solvents, including the kinetic and thermodynamic reasons for retained or altered activity in nonpolar environments.

Dynamics and Thermodynamic Contributions

• Quantitative Analysis of Catalysis:
  • Calculate how changes in free energy (ΔG‡) reflect the stabilization of the transition state versus the destabilization of the ground state, incorporating concepts like ground-state destabilization and pre-orientation.
• Assess the Role of Molecular Dynamics:
  • Describe how changes in torsion angles, distances, and dihedral angles (e.g., χ1 for Ser 195) are correlated with catalysis and substrate positioning.
• Relate Physical Chemistry to Biochemical Function:
  • Explain how fundamental physical and chemical principles (hydrogen bonding, entropy, van der Waals interactions, and torsional strain) contribute quantitatively to the overall catalytic rate enhancement.

Broader Applications and Synthetic Utility

• Enzyme Specificity and Selectivity:
  • Discuss how the specificity of chymotrypsin (and other enzymes) can change depending on the solvent environment, with implications for substrate binding and competitive inhibition.
• Practical Implications in Organic Synthesis:
  • Evaluate how enzymes used in organic solvents serve as stereoselective, regioselective, and chemoselective catalysts, and outline potential applications in novel organic transformations.

These learning goals provide a structured framework for understanding the multifaceted nature of enzyme catalysis, integrating detailed mechanistic insights with experimental evidence and quantitative analysis.

 

KristenProcko and HenryJakubowski have written this chapter section.

Introduction

To this point, we've presented mechanisms with the support of PDB structures alone. However, much was known about enzyme mechanisms before ready access to crystal structures in the Protein Data Bank. Systematically, the kineticists, medicinal chemists, and molecular biologists (i.e., well-trained chemists) can change:

1. the substrate - for example, changing the leaving group or substituents of a hydrolyzable substrate;
2. the pH or ionic strength - which can give data about general acids/bases in the active site;
3. the enzyme - by chemical modification of specific amino acids or through site-specific mutagenesis;
4. the solvent - an odd idea on the surface but it leads to new insights into enzyme catalysis.

We will concentrate on reaction mechanisms based on a mix of structural, kinetic, and thermodynamic data for the following enzymes to hypothesize a reaction mechanism consistent with the findings. Even with lots of data, there are often different proposed mechanisms for a given reaction. Kinetic data is vital as it can help to determine:

• the order of binding/dissociation of substrates and products;
• the rate constants for individual steps;
• and clues to the nature of catalytic groups found in the enzyme.

Chymotrypsin and Other Serine Proteases

Chymotrypsin (EC 3.4.21.1), an endoprotease, cleaves an internal peptide bond after aromatic side chains by hydrolysis. It also cleaves small ester and amide substrates after aromatic residues. For example, in Figure \(\PageIndex{1}\), cleavage occurs on the C-terminal side of the tyrosine residue, giving two peptide fragments.

Figure \(\PageIndex{1}\): Chymotrypsin cleavage of an example peptide substrate

Chymotrypsin has a similar mechanism to many other serine proteases that use the same catalytic triad, Ser 195, Asp 102, and His 95, so we'll study it in significant detail. In determining the mechanism of an enzyme, you have to change an experimental variable and see how catalytic activity changes. What can be changed? It turns out everything, including the solvent! Let's explore these changes and how they affect chymotrypsin activity.

1. Changing the substrate (for example, changing the leaving group or acyl substituents of a hydrolyzable substrate):

In the lab, studying the enzyme using small substrate mimics of a protein is easier than using a full protein substrate. The mimics include both esters and amides. Data from the small amide and ester substrates cleavage shown in Figure \(\PageIndex{2}\) suggest that a covalent intermediate is formed during chymotrypsin-catalyzed cleavage.

Figure \(\PageIndex{2}\): Small amide and ester substrates of chymotrypsin

Table \(\PageIndex{1}\) below shows kinetic data for the cleavage of these substrates.

Chymotrypsin substrate cleavage, 25 ^oC, pH 7.9
kinetic constants	Acetyl-Tyr-Gly-amide	Acetyl-Tyr-O Ethylester	Ester/Amide
kcat (s^-1)	0.50	193	390
Km (M)	0.023	0.0007	0.03
kcat/Km (M^-1s^-1)	22	280,000	12,700

Kinetic constants for chymotrypsin cleavage of N-acetyl-L-Trp Derivatives - N-acetyl-L-Trp-X
X	kcat (s^-1)	Km x 103 (M)
-OCH2CH3	27	0.097
-OCH3	28	0.095
-p-nitrophenol	31	0.002
-NH2	0.026	7.3

Table \(\PageIndex{1}\): Cleavage of peptides and ethylester substrate analogs by chymotrypsin

Here's how these data can be interpreted.

1. The k_cat and k_cat/K_m are larger and the K_m smaller for ester substrates compared to amide substrates, suggesting that amides are more challenging to hydrolyze (Table 2 above). This is expected given the poorer leaving group of the amide.
2. The k_cat for the hydrolysis of ester substrates doesn't depend on the nature of the leaving group (i.e., whether it is a poorer leaving group such as methoxy or a better leaving group such as p-nitrophenolate), suggesting that this step is not the rate-limiting step for ester cleavage. Without the enzyme, p-nitrophenyl esters are cleaved much more rapidly than methyl esters. Therefore, deacylation must be rate-limiting. But deacylation of what? If water were the nucleophile, releasing the leaving group would result in both products, the free carboxyl group and the amine, being formed simultaneously. Since they are not released simultaneously, this suggests an acyl-enzyme covalent intermediate.

A covalent intermediate can be trapped when the acyl end of the ester substrate is changed without changing the leaving group (a p-nitrophenyl group). Specifically, the deacylation of a trimethylacetyl group is much slower than that of an acetyl group. It is so slow that a ¹⁴C-labeled trimethylacetyl-labeled chymotrypsin intermediate can be isolated after incubation of chymotrypsin with ¹⁴C-labeled p-nitrophenyltrimethylacetate using gel filtration chromatography.

We have seen a kinetic mechanism previously consistent with these ideas before. The data suggest a mechanism based on the chemical equations shown in Figure \(\PageIndex{3}\):

Figure \(\PageIndex{3}\): Chemical equations for chymotrypsin hydrolysis of a substrate involved a covalent intermediate with ping-pong kinetics.

In this reaction, a substrate S might interact with E to form a complex, which then is cleaved to products P and Q. Q is released from the enzyme, but P might stay covalently attached until it is expelled. This conforms exactly to the mechanism described above. For chymotrypsin-catalyzed cleavage, the step characterized by k₂ is the acylation step. The step characterized by k₃ is the deacylation step in which water attacks the acyl-enzyme to release product P (free phosphate in Lab 5). The mathematical equation for this reaction is shown below (without derivation)

\begin{equation}
\mathrm{v}_{0}=\frac{\left(\frac{\mathrm{k}_{2} \mathrm{k}_{3}}{\mathrm{k}_{2}+\mathrm{k}_{3}}\right) \mathrm{E}_{0} \mathrm{~S}}{\mathrm{~K}_{\mathrm{S}}\left(\frac{\mathrm{k}_{3}}{\mathrm{k}_{2}+\mathrm{k}_{3}}\right)+\mathrm{S}}
\end{equation}

For hydrolysis of ester substrates, which have better leaving groups than amides, deacylation is rate limiting ( k₃<<k₂). For amide hydrolysis, as mentioned above, acylation can be rate-limiting (k₂<<k₃). From this, equation 6.5.1 can be simplified as shown in Table \(\PageIndex{2}\) below for ester and amide hydrolysis.

Ester hydrolysis (deacylation rate limiting, k3 << k2)	Amide hydrolysis (deacylation rate limiting, k2 << k3)
\begin{equation} \mathrm{v}_{0}=\frac{\mathrm{k}_{3} \mathrm{E}_{0} \mathrm{~S}}{\mathrm{~K}_{\mathrm{S}}\left(\frac{\mathrm{k}_{3}}{\mathrm{k}_{2}}\right)+\mathrm{S}} \end{equation}	\begin{equation} \mathrm{v}_{0}=\frac{\mathrm{k}_{2} \mathrm{E}_{0} \mathrm{~S}}{\mathrm{~K}_{\mathrm{S}}+\mathrm{S}} \end{equation}
\begin{equation} V_{M}=k_{3} E_{0} \end{equation}	\begin{equation} \mathrm{V}_{\mathrm{M}}=\mathrm{k}_{2} \mathrm{E}_{0} \end{equation}
\begin{equation} \mathrm{K}_{\mathrm{M}}=\mathrm{K}_{\mathrm{S}}\left(\frac{\mathrm{k}_{3}}{\mathrm{k}_{2}}\right) \end{equation}	\begin{equation} \mathrm{K}_{\mathrm{M}}=\mathrm{K}_{\mathrm{S}} \end{equation}

Table \(\PageIndex{2}\): Simplification of equation 6.5.1

As we saw before, for the rapid equilibrium assumption (when ES falls apart to E + S more quickly than it goes to the product, Chapter 6.3), K_M = Ks in the case of amide hydrolysis.

This reaction with two reactants (bi) and two products (bi), a covalent enzyme intermediate with the second reactant binding after the first product Q is released, is called a BiBi Ping Pong reaction.  If k₂ >> k₃, an immediate and fast burst or release of product Q happens, followed by a slow release of P since the covalent E-P complex reacts with the second reactant with a small rate constant k₃.  When doing initial rate Michaelis-Menten kinetics, the initial velocity of Q formation, v₀, is not (dQ/dt)_t=0, but the slower constant rate after the burst phase, which is determined by k₃, the rate of cleavage of the E-P intermediate.     

The VCell computational model below shows the reaction BiBi Ping Pong reaction for the reaction involving an enzyme-P covalent intermediate.  The burst phases in Q is clearly seen if you rescale the graph as described below.

---

MODEL

BiBi-Ping Pong_Covalent Intermediate Irreversible reaction

Vcell reaction diagram (1-way arrows defined as reversible in actual mathematical model) and chemical equation

Yellow dots: Reaction Nodes (R1, R2 and R3 left to right)

Reaction made irreversible since k_r2 = 0, k_r3 = 0.

Initial parameter values:

• S₀ = 100, E₀ = 1, W (water in a hydrolysis reaction) = 50 and fixed throughout
• k_1f = 5, k_1r = 1, k_2f = 0.6,
• k_2f = 50, k_2r = 0
• k_3f = 0.05, k_3f = 0

Select Load [model name] below

 Select Start to begin the simulation.

1Interactive Element

Select Plot to change Y axis min/max, then Reset and Play  |  Select Slider to change which constants are displayed |  Select About  for software information.

To see the burst phase for reaction, change the time and parameters to these values:

• set Run time to 0.3
• Select Plot then Update Y axis max to 2
• Click Edit Plot Species and check just P and Q
• reset

Time course model made using Virtual Cell (Vcell), The Center for Cell Analysis & Modeling, at UConn Health.  Funded by NIH/NIGMS (R24 GM137787); Web simulation software (miniSidewinder) from Bartholomew Jardine and Herbert M. Sauro, University of Washington.  Funded by NIH/NIGMS (RO1-GM123032-04)

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The burst phase is seen with ester hydrolysis as described above when k₂ >> k₃.

2. Changing the pH or ionic strength - which can give data about general acids/bases in the active site:

• a graph of k_cat as a function of pH indicates that a group of pK_a of approximately 6 must be deprotonated to express activity (i.e., V_max/2 is at about pH 6). This suggests that an active site histidine is necessary, which, if it must be deprotonated to express activity, must be acting as a general base.
• a graph of k_cat/K_m shows a bell-shaped curve indicating the necessity of a deprotonated side chain with a pK_a of about 6 (i.e., the same His above) and a group that must be protonated with a pK_a of about 10. This is an N terminal Ile in chymotrypsin, which must be protonated to form a stabilizing salt bridge in the protein. Note: This N-terminal Ile is actually at the 16 position in the inactive precursor of chymotrypsin (called chymotrypsinogen); upon activation of chymotrypsinogen, it loses the first 15 amino acids by selective proteolysis.

(Note: The PKAD is a database of experimentally measured pK_a values of protein ionizable groups. It is searchable by the PDB ID.)

3. Changing the enzyme - by chemical modification of specific amino acids, or through site-specific mutagenesis:

Here are some specific examples.

1. Modification of chymotrypsin (and many other proteases) with diisopropylphosphofluoridate (DIPF) modifies only one (Ser 195) of many serines in the protein, suggesting that it is hypernucleophilic and probably the amino acid that attacks the carbonyl C in the substrate, forming the acyl-intermediate. This reaction is illustrated in Figure \(\PageIndex{3}\). The figure also shows analogous molecules used in common insecticides, which act through a similar mechanism.

Figure \(\PageIndex{3}\): Mechanism of chymotrypsin inhibition by covalent modification by diisopropylphosphoflouridate.

2. Modification of the enzyme with tos-L-Phe-chloromethyl ketone inactivates the enzyme with a 1:1 stoichiometry, which results in a modified His, as shown in Figure \(\PageIndex{4}\).

Figure \(\PageIndex{4}\): Reaction of chymotrypsin and other serine protease with chloromethyketones.

3. A comparison of the primary sequences of many proteases shows that three residues are invariant: a Ser, a His, and an Asp.
4. Site-specific mutagenesis shows that if Ser 195 is changed to Ala 195, the enzymatic activity is almost reduced to background levels. This strongly suggests that Ser 195 is an active site nucleophile.

D. Changing the solvent. Yes, indeed, you can take chymotrypsin and show that it is active in anhydrous organic solvents. Surely this is impossible, you say! It is true, and we will explore it at the end of the chapter since it's challenging enough to understand chymotrypsin activity in an aqueous solution. No new chemistry is needed; it is just a change in what you can conceptualize.

Quantitative Analysis of Catalysis by Serine Proteases 

Based on Siyuan Du et al. Conformational ensembles reveal the origins of serine protease catalysis. Science 387, eado5068 (2025). DOI:10.1126/science.ado5068.

Our understanding of enzyme catalysis is incomplete. Other factors, in addition to those described in Chapter 6.1: How Enzymes Work, likely contribute to the 10¹² increase in the rate of serine protease-catalyzed hydrolysis of peptide bonds compared to solution hydrolysis. A quantitative analysis of each factor would help define its contribution and help find new ones. Siyuan et al. have done just that.

So far, we've seen that the active site serine side chain (pKa ≈ 13, not considering its environment) acts as a nucleophile, made better by a nearby general base/acid histidine (pKa ≈ 7), which, after proton abstraction to form His⁺, is stabilized by a nearby negatively-charged aspartate. The developing δ^- on the carbonyl O in the transition state and the intermediate's full negative oxyanion are stabilized in the "oxyanion hole" through hydrogen bonds from N-H main chain donors, Ser 193 and Gly 195 (pKa ≈ 15). The reaction is intramolecular (entropically favored over bimolecular reactions) after substrate binding, except for the reaction with solvent water (55 M) needed to complete the reaction.  

Now compare this to the uncatalyzed hydrolysis in water.  H₂O (pKa ≈ 16) is the nucleophile/substrate, and other waters (pKa ≈ 16) stabilize the developing δ^-O in the transition state and the oxyanion intermediate. By analogy to the enzyme-catalyzed reaction, a stabilizing water molecule, which becomes, on accepting a proton, H₃O⁺ (pKa ≈ -2) increases the nucleophilicity of the "substrate" water by proton abstraction. 

Except for the adjacent His (pKa ≈ 7), which can more readily act as a general acid/base), there is nothing extraordinary about the groups involved in catalysis.  The constrained intramolecular reaction involving the positioning and likely distortion of substrates in the active site is a critical feature to quantify.  Another factor we haven't discussed is the dynamics of the reaction.  The reaction has to proceed along reaction coordinates involving bond-making and breaking.  In addition, substrates, waters, and side chains move to position themselves for catalysis.  

Siyuan Du et al. show that fundamental concepts in chemistry and physics (torsion angles and strain, van der Waals interactions, hydrogen bonds, and entropy) can explain catalysis. They state that this "simplicity may inspire new ways of teaching enzyme catalysis, allowing instructors to reinforce the value of fundamental physical and chemical concepts and students to appreciate the tight connection between these concepts and the emergent, complex functions of biomolecules."  This is precisely what Fundamentals of Biochemistry attempts to do!  

They used molecular dynamics simulations and protein structures to analyze contributions to catalysis quantitatively. Although we'll focus on serine proteases here, they extended their analyses to other enzymes.  They compared the PDB structures of 1231 wild-type serine proteases from 4 clans (structural superfamilies).  These structures included enzymes:

• without substrate or other ligands (i.e. the apo form of the enzyme);
• with bound ligand when the ligand structure is unperturbed (i.e., the ligand is a ground-state analog or GSA) which is typically a noncovalently-bound peptide or peptide analog);
• with covalently bound ligands resembling the transition state for a substrate (i.e., the ligand is a transition state analog or TSA).  The enzyme's active site would have a slightly altered structure to accommodate the tetrahedral TSA.  The TSAs are covalently attached to Ser 195 through an sp³ tetrahedral bond.  These TSAs include fluoromethylketones, peptide aldehydes, and boronic acids, which underwent nucleophilic addition at the analog's sp² carbonyl carbon or boron center as they form adducts.  The attached TSA stays covalently attached and does not react further.  The active site differs from the apo and GSA-bound form from the movement required to form the covalent adduct.  The active site is trapped in an "active" conformation.

These 1231 structures form a group or "pseudo-ensemble," which collectively provides data that have been hidden until the present analysis. These data describe subtle factors favoring catalysis and hint at the dynamical motion required within the active site, where groups move from the apo state to the transition/intermediate state. 

Quantum mechanical analyses of reaction paths and dynamics for the hydrolysis reaction of N-methylacetamide (NMA) in water (without enzyme) were studied for a meaningful comparison to the solution-phase reaction.  (We saw NMA in Chapter 4.9: Protein Stability - Thermodynamics.) NMA mimics the peptide bond as shown below in Figure \(\PageIndex{5}\) below.  It likewise forms a tetrahedral intermediate during hydrolysis. 

Figure \(\PageIndex{5}\): Comparison of N-methylacetamide to a peptide bond.

Molecular dynamics simulations were used to obtain a distribution or ensemble of reacting molecules in solution to parallel the ensemble of protein structures.  

They then compared the distribution of molecules (solution) and sidechains (enzyme) to compare the positioning of the serine side chain (compared to water), as catalysis has to involve its movement.  Three geometric variables were used: the distance (d_attack), angle (α_attack) and dihedral (Φ_attack). These parameters are described in Figure \(\PageIndex{6}\) below.

Figure \(\PageIndex{6}\): Visual representations of 3 key geometric parameters for hydrolysis of amide bonds.

Panel A shown d_attack, the distance between the nucleophile O on serine (or water in the uncatalyzed case) and the electrophilic C on the amide substrate, and α_attack, the angle between three atoms (the nucleophilic O, the electrophilic C, and the carbonyl O. The other key angle is a dihedral.  Panel B reviews examples of a dihedral angle.  The left Newman project shows the Φ dihedral, which is the angle of rotation around the C_b-C_c bond in the four atoms, three bonds C_a-C_b-C_c-C_d structure, where C_b is the front carbon, and C_c is the back carbon represented by the blue circle.  The right structure shows that the Φ_dihedral is also the angle of rotation around the red dotted line (---) connecting two gray planes.  Panel C shows the Φ_{attack.  In this} case, the gray plane contains the sp² hybridized amide substrate, and the red-dotted plane/triangle contains the plane defined by the nucleophilic O, the electrophilic C, and the carbonyl O.

The values for these parameters were very similar for all serine proteases studied with mode (not median) values as follows: d_attack = 2.68 Å (SD = 0.14 Å), α_attack = 93° (SD = 7°), and Φ_attack = 84° (SD = 8°).  The distribution in water for the nucleophilic attack of water on DMA was much broader, and the distance was larger.  So, it seems that the serine in proteases has a shorter path and higher efficiency for attack.  A caveat is that the active site can't be too rigid, which could hinder the motions required for catalysis.  Also, the serine must be pointed in the right direction.

To look for catalytic-specific motion, they compared torsion angles (backbone, side chain) for every residue in the enzyme with GSA and TSA bound. In addition, they measured changes between the apo and GSA-bound enzyme to see changes just on the binding substrate.  Differences among these were interpreted as movement along the reaction pathway.  For trypsin, 32 torsion angle changes were found when substrate bound, and 23 were found for nucleophilic attack (comparing TSA and GSA-bound enzymes).  These changes were distributed throughout the enzyme.  Changes in the torsion angle χ¹ for the Cα–Cβ in the side chain of Ser 195 were large and occurred during substrate binding (−14°, leading to torsional strain on partial eclipsing) and the actual nucleophilic attack (+14°, relieving the torsional strain).  This large change was also seen for chymotrypsin and elastase (in the same clan).  Indeed, this common single change was the single largest torsional change for the 3 enzymes.

Figure \(\PageIndex{7}\) shows an interactive iCn3D model of the alignment of bovine pancreatic trypsin with a Kunitz Type serine protease Inhibitor-1 (3M7Q), a ground state noncovalent inhibitor and trypsin with APA (1TPP), a covalent transition state analog (TSA). The gray backbone is the GS inhibitor complex, and the cyan backbone is the TSA analog covalent complex.  The inhibitors are not shown for clarity and simplicity.  Toggle the "A" key to switch between each form.

 Figure \(\PageIndex{7}\): Kunitz Type serine protease Inhibitor-1 (3M7Q), a ground state noncovalent inhibitor and trypsin with APA (1TPP), a covalent transition state analog. (Copyright; author via source).  Click the image for a popup or use this external link: https://www.ncbi.nlm.nih.gov/Structu...pUFy1femfcy4Y7

Look at the change in orientation of the serine O nucleophile.  Rotate the models to see distance and  χ¹ since the side chain dihedral angle changes.

In the GSA-Trypsin, the nucleophilic Ser-O to the electrophilic carbonyl carbon in the planar sp² peptide bond is 2.7 Å (open this iCn3D link to see the distance).  The van der Waals radius for a carbonyl carbon (C) ≈ 1.7 Å, and ≈ 1.52 Å for an O, so the optimal distance is 3.2 Å.  Hence, the ground state structure is partially destabilized before bond-making actually occurs. The destabilization in the GSA contributes to catalysis.

A distance change occurs in the TSA complex as the serine oxygen moved ≈ 0.3 Å closer to the electrophilic carbon (now sp³), which is now raised 0.8 Å above the plane from its previous position in the sp² substrate since it is attached to the C. This move is expected during the dynamic progress of the reaction as it proceeds along the reaction path. Now, the distance from the Ser-O to the electrophilic carbon in the covalent tetrahedral sp³ (nonplanar) TSA adduct is 1.6 Å (open this iCn3D link to see the distance).  (Note: the paper gives values of 1.6 in the text and 1.7 in a figure.) The net movement is ≈ 1.1 Å movement. 

How does this compare to the solution hydrolysis path?  Quantum mechanical analyses show that the distance between the water O and the NMA electrophilic C in the substrate in solution is 3.6 Å, greater the the vdW distance.  This decreases  ≈ 2 Å, not ≈ 1.1 Å, as we saw for the enzyme reaction.  No bond rotations are noted.  Most of the changes arise from a simple translation of the nucleophilic O on the water, which is farther from the electrophilic carbon in the ground state.  Hence, the enzyme has a shorter reaction path with part contributed by 1D bond dihedral rotation, faster than positioning the reactants with a 3D translation.

Let's translate some of these changes into the thermodynamics parameter ΔG. Rates of catalysis can be related to the equilibrium constant, which is related to the ΔG⁰ for the reaction.  For example, suppose that breaking a strong bond is rate limiting in a pathway, which often occurs in a thermodynamically stable molecule that reacts. In that case, the reaction rate also depends on the bond strength (i.e., a measure of its thermodynamic stability). For acids and bases, this is reflected in a linear relationship between log(k), the rate constant for the reaction, and the log(K_a), the equilibrium acid constant, as shown by the linear  Bronsted catalysis equation below:

\begin{equation}
\log k=\operatorname{alog}\left(K_{\mathrm{a}}\right)+C=-a p K_a+C
\end{equation}

ΔG for individual catalytic steps can be calculated using this linear free energy relationship example.  For example, the observed 10⁶ increase in rate for trypsin from the histidine general base catalysis and its high effective intramolecular concentration gives a value of ΔG around 8.2 kcal/mol with an extra 0.8 kcal/mol from the stabilizing catalytic triad aspartate. The overall 10¹² increase in catalytic rate (net 17.1 kcal/mol) suggests another 8.1 kcal/mol remains unexplained.  The authors attribute the remaining catalysis to several factors.

One feature is based on the ground state of the enzyme.  When the substrate binds, and since the reaction proceeds in an intramolecular fashion, there is reduced conformational entropy and some unfavorable interactions, as described above.  These are decreased (relieved) in the transition site.  The net effect is another 7.6 kcal/mol of catalysis. They refer to these combined effects as ground-state destabilization.

Let's consider all of the factors they explored.  The first two deal with the entropy of positioning both the reactant and the active site serine:

• pre-orientation of the reactant in the active site: This makes it entropically easier to reach the "single" transition state than the reaction in water.
• pre-orientation of the enzyme serine nucleophile: Similarly, pre-orientation of the serine nucleophile in the vicinity of the substrate decreases the number of possible microstates needed to reach the transition state, entropically favoring the reaction.
• ground state destabilization of the complex through O-C bond shortening:  We mentioned above that the serine O to carbonyl C distance is shorter than the van der Waals interaction distance, which raises its energy as it moves into the direction of the transition state.
• ground state destabilization of the complex through partial eclipsing from the torsion angle of the catalytic serine:  As mentioned above, this rotation is reversed on conversion to the transition state. 
• ground state destabilization of the main oxyanion hole by hydrogen bonds:  Solution phase H bonds between amide Hs and carbonyl Os are more stable when planar. In the GSA, they are not planar and hence destabilized. 

The authors calculated  ΔG for each of these effects.  For an enzymatic reaction, the free energy of the transition state ΔG‡_solution > ΔG‡_enzyme.  The following equation describes ΔΔG‡:

\begin{equation}
\Delta \Delta \mathrm{G}^{\ddagger}=\Delta \mathrm{G}^{\ddagger}{ }_{\text {solution }}-\Delta \mathrm{G}^{\ddagger}{ }_{\text {enzyme }}
\end{equation}

Hence, the ΔΔG‡ value for the enzyme-catalyzed reaction and each contributing factor are all positive (>0). Figure \(\PageIndex{8}\) shows the individual contributions (combined to 16.6 kcal/mol) compared to the experimentally observed value of 17 kcal/mol.

Figure \(\PageIndex{8}\):  Data from Siyuan Du et al., ibid.  Error bars not included. 

Within error, catalysis can be described by destabilizing the ground state substrate and stabilizing the transition state based on principles you learned in introductory and organic chemistry: acid/base reactions, hydrogen bonds, entropy, torsional strain, bond angle strain, and van der Waals interactions.  The authors extended their analyses and found the same factors account for catalysis by other enzymes of distinct folds using nucleophilic attack on carbonyl carbons.  These include lactamases, caspases, transcylases, acylases, peptidases, and other proteases.  They found similar structures and catalytic features (listed above) when aligning the PDB structures on active site nucleophiles, oxyanion holes, oxyanion, and the substrates electrophile carbon.  

Enzyme catalysis in organic solvents

In our earlier lists, we mentioned changing the solvent and exploring its effect on enzyme catalysis. It might seem a bit wild, but as we saw with the rhomboid protease, some enzymes work in hydrophobic environments. Also, lipases work at the boundary between the aqueous and hydrophobic worlds. For those interested, let's see what happens when we change solvents. These include putting the enzyme in various solvents or mixtures of solvents, as described below:

• Water-miscible solvents like ethanol and acetone were added. If the water concentration was high enough, activity remained.
• Biphasic mixtures in which an aqueous solution of an enzyme was emulsified in a water-immiscible solvent like chloroform or ethyl acetate. The substrate would partition into both phases, while the product hopefully would end up in the organic phase.
• Nearly nonaqueous solvents, with a few % water at less than the solubility limits of water.
• Anhydrous organic solvents (0.01% water). This case is most astonishing since enzymatic activity is often retained.

It is important to realize that in this last case, the enzyme is not in solution. Instead, it is in suspension and acts as a heterogeneous catalyst, much like palladium, which acts as a heterogeneous catalyst in the hydrogenation of alkenes. The suspension must be mixed vigorously and then sonicated to produce small suspended particles, so diffusion of reactants into the enzyme and out is not rate limiting. Let's explore the activity of chymotrypsin in a nonpolar solvent.

Why aren't the enzymes inactive? Indeed, it must seem ridiculous that they aren't since, as we learned earlier, proteins are marginally stable. On average, a 100 amino acid protein is stabilized only about 10 kcal/mol (41 kJ/mol) over the denatured state, or the equivalent of a few H bonds. Indeed, the hydrophobic effect, one of the dominant contributors to protein folding and stability, would not stabilize the native structure of enzymes in nonpolar organic solvents, and the protein would denature. It doesn't, however! Maybe the real question should be not whether water is necessary but how much water is essential. The enzyme can't "see" more than a monolayer or so of water around it. The data suggests that the nature of the organic solvent is very important. The most hydrophobic solvents are best in terms of their ability to maintain active enzymes! Chymotrypsin retains 10⁴ more activity in octane than pyridine (see k_cat/K_m below), which is more hydrophilic than octane. The more polar the solvent, the more it can strip bound water away from the protein. If you add 1.5% water to acetone, the bound water increases from 1.2 to 2.4%, and the activity of chymotrypsin increases 1000-fold.

Table \(\PageIndex{3}\) below shows chymotrypsin activity in organic solvents.

Solvent	Structure	kcat/Km (M^-^1min^-1)	relative ratio kcat/Km	H2O bound to enzyme (%, w/w)
Octane		63	15000x	2.5
Toluene		4.4	1000x	2.3
Tetrahydrofuran		0.27	175x	1.6
Acetone		0.022	5.5x	1.2
Pyridine		<0.004	1x (.004)	1.0

Table \(\PageIndex{3}\): Chymotrypsin activity in organic solvents

Consider the following questions:

• How much water do the enzymes need? One chymotrypsin molecule in octane has less than 50 molecules of water associated with it and can demonstrate activity. About 500 water molecules are required to form a monolayer. Water can be added, presumably leading to more water binding and higher activity.
• How stable are the enzymes? Denaturation requires conformational flexibility, which requires water. The half-life of chymotrypsin in water at 60 ^oC is minutes, but in octane at 100 ^oC, it is hours. At 20 ^oC, the half-life in water is a few days, but in octane, it is greater than 6 months. Remember two factors contribute to stability: 1. The protein can denature at high temperatures. 2. Chymotrypsin is a protease. It can cleave itself in an autoproteolytic reaction.

Table \(\PageIndex{4}\) below shows the half-life of chymotrypsin activity in water and octane

Solvent	60^oC	100^oC	20^oC
water	minutes	-	few days
octane	-	hours	> 6 months

Table \(\PageIndex{4}\): Half-life of chymotrypsin activity in water and octane at different temperatures

• Has the enzyme specificity changed? The net binding energy is a function of the substrate's binding energy minus the water's binding energy since water must be displaced from the active site on binding. In an anhydrous solvent, specificity changes must be expected. For chymotrypsin, the driving force for binding substrates in water is primarily hydrophobic. In water, the k_cat/K_M for the reaction of N-acetyl-L-Ser-esters is reduced 50,000 times compared to the Phe ester. However, chymotrypsin is three times more active toward Ser esters in octane than Phe esters.

Table \(\PageIndex{5}\) shows specificity changes in chymotrypsin in water and octane

Substrate	kcat/Km
	solvent: H2O	solvent: Octane
N-acetyl-L-Ser-ester	1x	3x
N-acetyl-L-Phe-ester	50,000x	1x

Table \(\PageIndex{5}\): Specificity changes in chymotrypsin in water and octane

Now, consider competitive inhibitors. Naphthalene binds 18 times more tightly than 1-naphthoic acid, but chymotrypsin binds naphthoic acid 310 times as tightly in octane. Likewise, the ratio of [k_cat/K_m (L isomer)]/[k_cat/K_m (D isomer)] of N-acetyl-D- or N-acetyl-L-Ala-chloroethyl esters is 1000-10,000 in water, but less than 10 in octane.

Table \(\PageIndex{6}\) shows chymotrypsin inhibition constants in water and octane.

Inhibitor	Inhibition Constant Ki (nM)
	In water	In Octane
Benzene	21	1000
Benzoic acid	140	40
Toluene	12	1200
Phenylacetic acid	160	25
Naphthalene	0.4	1100
1-Naphthoic acid	7.2	3

Table \(\PageIndex{6}\): Chymotrypsin inhibition constants in water and octane

Can new reactions be carried out in nonpolar solvents? The quick answer is yes since reactions in aqueous solutions can be unfavorable due to low K_eq values, side reactions, or insolubility of reactants. Consider lipases, which cleave fatty acid esters by hydrolysis in aqueous solutions. In nonaqueous solutions, reactions such as transesterification or ammonolysis can be performed.

Enzymes are active in organic solvents, which contradicts our central concepts of protein stability. Two reasons could could explain this stability:

1. From a thermodynamic perspective, the enzyme may be stable in organic solvents. However, as discussed above, this is inconceivable given the delicate balance of noncovalent and hydrophobic interactions required for protein stability.
2. The second reason must prevail: the protein cannot unfold from a kinetic point of view. Conformational flexibility is required for denaturation, which requires water as the solvent. Denaturation in organic solvents is kinetically, not thermodynamically, controlled.

A specific example helps illustrate the effects of different solvents on chymotrypsin activity. Dry chymotrypsin can be dissolved in DMSO, a water-miscible solvent. In this solvent, chymotrypsin is entirely and irreversibly denatured. No activity is observed if it is now diluted 50X with acetone with 3% water. (In the final dilution, the concentrations of solvents are 98% acetone, 2.9% water, and 2% DMSO.) However, the enzyme is very active if dry chymotrypsin is added to a mixture of 98% acetone, 2.9% water, and 2% DMSO. We end up with the same final solvent state, but the enzyme has no activity in the first case, while in the second case, it retains activity. These ideas are illustrated in Figure \(\PageIndex{9}\).

Figure \(\PageIndex{9}\): Chymotrypsin activity in acetone depends on the order of solvent addition

Dry enzymes added to a concentrated water-miscible organic solvent (like DMSO) will dissolve and surely denature but will retain activity when added to a concentrated water-immiscible solvent (like octane), in which the enzyme will not dissolve but stay in suspension.

It appears the enzymes have very restricted conformational mobility in nonpolar solvents. By lyophilizing (freeze-drying) the enzyme against a specific ligand, a given conformation of a protein can be trapped or imprinted onto the enzyme. For example, if the enzyme is dialyzed against a competitive inhibitor (which can be extracted by the organic solvent), freeze-dried to remove water, and then added to a nonpolar solvent, the enzyme activity of the "imprinted" enzyme in nonpolar solvents is as much as 100x as great as when no inhibitor was present during the dialysis. Suppose chymotrypsin is lyophilized from solutions of different pHs. In that case, the resulting curve of V/Km for ester hydrolysis in octane is bell-shaped, with the initial rise in activity reaching half-maximum activity at a pH of around 6.0 and a fall in activity reaching half-maximum at a pH of approximately 9.

The use of enzymes in organic solvent allows new routes to organic synthesis. Enzymes, which are so helpful in synthetic reactions, are:

• stereoselective - can differentiate between enantiomers and between prochiral substrates
• regioselective - can differentiate between identical functional groups in a single substrate
• chemoselective - can differentiate between different functional groups in a substrate (such as between a hydroxyl group and an amine for an acylation reaction)

Enzymes in anhydrous organic solvents are useful (from a synthetic point of view) not only because they can catalyze new types of reactions (such as transesterification, ammonolysis, and thiolysis) but also because the stereoselectivity, regioselectivity, and chemoselectivity of the enzyme often differ from those of the enzyme in water.

Organic reactions are usually conducted in organic solvents since many organic molecules react with water, and the reagents and products are generally not soluble in water. In a manner analogous to using an enzyme as a heterogeneous catalyst in a nonpolar solvent, Sharpless is pioneering a technique to conduct organic reactions in water. They (Narayan et al.) have shown that many unimolecular and bimolecular reactions occur faster in water than in organic solvents. As in enzyme catalysis in nonpolar solvent, the reactions must be mixed vigorously to disperse reactants in micro-drops (a suspension) in water, significantly increasing the surface area that might allow water to act on transition states or intermediates to stabilize them through hydrogen bonding. They called these "on water" reactions since reactants usually float on water. Using this process, they have performed cycloadditions, alkene reactions, Claisen rearrangements, and nucleophilic substitution reactions. One cycloaddition reaction went to completion in ten minutes at room temperature, compared to 18 hours in methanol and 120 in toluene. Adding nonpolar solvents at certain times significantly increased the rate of the reaction.

Summary

This chapter explores the mechanistic and thermodynamic foundations of enzyme catalysis with an emphasis on serine proteases—particularly chymotrypsin. It demonstrates how a combination of structural, kinetic, and thermodynamic data can be employed to develop detailed reaction mechanisms, even before the advent of high-resolution crystal structures.

Enzyme Mechanisms and the Catalytic Triad

• Catalytic Strategy:
  The chapter begins by describing how early enzyme mechanism studies relied on kinetic experiments and chemical modifications to elucidate catalytic strategies. In serine proteases, the catalytic triad—comprising Ser 195, His (57/95), and Asp 102—is critical. Ser 195 acts as a nucleophile, His functions as a general base, and Asp stabilizes the positive charge on His.

• Evidence for Covalent Intermediates:
  Kinetic analyses using small ester and amide substrates reveal that chymotrypsin forms a covalent acyl-enzyme intermediate. Differences in k_cat and k_cat/K_m values between ester and amide substrates, along with substrate modifications (e.g., changing leaving groups), support this mechanistic hypothesis.

Kinetic Analysis and the Ping Pong Mechanism

• BiBi Ping Pong Kinetics:
  The reaction is characterized by a burst phase—rapid formation of an initial product followed by a slower phase corresponding to deacylation. This two-step process is described by a simplified kinetic model that distinguishes between acylation (k₂) and deacylation (k₃) steps. Depending on which step is rate-limiting, the kinetic equations can be simplified for ester or amide hydrolysis.

• Mathematical Modelling:
  The chapter outlines the derivation of kinetic equations that link substrate concentration, enzyme concentration, and rate constants, allowing for a quantitative dissection of each catalytic step.

Modulation of Catalysis: Substrate, pH, and Enzyme Modifications

• Substrate Effects:
  Modifying the substrate’s leaving group or acyl substituents alters the kinetic parameters, thereby providing insight into the chemical steps of the reaction, such as the formation and breakdown of the acyl-enzyme intermediate.

• pH and Ionic Strength:
  pH-dependent studies reveal the involvement of ionizable groups. For instance, the activity profiles indicate that a deprotonated histidine is necessary for optimal catalysis, while other groups (e.g., the N-terminal Ile) contribute to structural stabilization through salt bridge formation.

• Enzyme Modifications:
  Chemical modification (using reagents like diisopropylphosphofluoridate) and site-specific mutagenesis confirm the essential roles of specific amino acids in the active site. Inactivating modifications that target Ser 195 or His validate their roles in nucleophilic attack and proton transfer.

The Role of Solvent in Enzyme Catalysis

• Aqueous vs. Organic Environments:
  A striking portion of the chapter is devoted to examining how chymotrypsin operates in nonaqueous solvents. In water-miscible and nearly nonaqueous solvents, the enzyme retains activity, whereas in anhydrous organic solvents it acts as a heterogeneous catalyst. The enzyme’s minimal hydration shell is sufficient for catalysis, and its kinetic stability can even increase due to the restricted conformational flexibility in nonpolar environments.

• Effects on Specificity and Inhibition:
  Solvent changes impact substrate specificity and inhibitor binding. For example, substrate preference shifts in octane compared to water, and competitive inhibitors display different binding affinities, underscoring how the solvent environment can influence enzyme–substrate interactions.

Quantitative Contributions to Catalysis

• Thermodynamic Perspective:
  The chapter concludes with a quantitative analysis that breaks down the contributions to the overall rate enhancement of serine proteases. Key factors include the stabilization of the transition state, pre-orientation of the reactants, and ground state destabilization upon substrate binding. Using linear free energy relationships (e.g., Bronsted relationships), the authors correlate changes in catalytic rate with specific free energy contributions, ultimately accounting for nearly the entire observed rate acceleration.

• Molecular Dynamics and Structural Ensembles:
  Analyses of PDB-derived structural ensembles and molecular dynamics simulations illustrate how subtle conformational changes (such as torsion angle adjustments in the catalytic serine) and geometric parameters (attack distances and angles) are finely tuned for catalysis, setting the enzyme apart from the uncatalyzed reaction in solution.

By integrating experimental data with computational modeling, the chapter not only deepens our understanding of enzyme catalysis at a molecular level but also highlights the interplay between structure, dynamics, and energetics. This comprehensive approach reinforces the idea that fundamental chemical principles—such as acid/base chemistry, hydrogen bonding, entropy, and van der Waals forces—are central to the sophisticated function of enzymes, inspiring new ways of teaching and exploring biomolecular catalysis.